Help Solving Equation Involving A Rational Exponential

[Captain1024]

Homework Statement

Solve $y=\mathrm{exp}(\frac{-x\pi}{\sqrt{1-x^2}})$ for x when y = 0.1

Homework Equations

$\mathrm{ln}(e^x)=x$

The Attempt at a Solution

$\mathrm{ln}(0.1)=\frac{-x\pi}{\sqrt{1-x^2}}$
$(\frac{-\mathrm{ln}(0.1)}{\pi})^2=\frac{x^2}{1-x^2}$

 

[ehild]

Homework Statement

Solve $y=\mathrm{exp}(\frac{-x\pi}{\sqrt{1-x^2}})$ for x when y = 0.1

Homework Equations

$\mathrm{ln}(e^x)=x$

The Attempt at a Solution

$\mathrm{ln}(0.1)=\frac{-x\pi}{\sqrt{1-x^2}}$
$(\frac{-\mathrm{ln}(0.1)}{\pi})^2=\frac{x^2}{1-x^2}$

It is all right so far. What is your problem? You got a simple equation for x².

 

[SammyS]

Homework Statement

Solve $y=\mathrm{exp}(\frac{-x\pi}{\sqrt{1-x^2}})$ for x when y = 0.1

Homework Equations

$\mathrm{ln}(e^x)=x$

The Attempt at a Solution

$\mathrm{ln}(0.1)=\frac{-x\pi}{\sqrt{1-x^2}}$
$(\frac{-\mathrm{ln}(0.1)}{\pi})^2=\frac{x^2}{1-x^2}$

One thing that will improve the looks of the right hand side. Recognize that −ln(0.1) is ln( (0.1)⁻¹ )

Another thing you might try is to take the reciprocal of both sides of the equation.

 

[Captain1024]

One thing that will improve the looks of the right hand side. Recognize that −ln(0.1) is ln( (0.1)⁻¹ )

Another thing you might try is to take the reciprocal of both sides of the equation.

$x=\sqrt{\frac{1}{\frac{\pi ^2}{(\mathrm{ln}(10))^2}+1}}$

That's what I needed. Thank you.